Cottonwood Elementary: math

The shaded band is this school's normal range. If nothing about how it works changes, nearly every future year should land inside it. Zero means the typical student just meets the state standard. The small numbers under the years are how many students were tested.

Step 1 · Each year's result

For each grade tested, take the average (mean) scale score from the California Department of Education's results file, and subtract the lowest score that counts as "Standard Met" for that grade. That is the grade's distance from standard. Weight each grade by its share of the students tested, then add the grades up. Grades where the state hides the average because ten or fewer students tested are left out entirely.

2015 from sb_ca2015_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	56,540	2432.3	− 2436	−3.7	× 27 / 181	−0.6
4	56,543	2490.2	− 2485	5.2	× 27 / 181	0.8
5	56,544	2513.0	− 2528	−15	× 40 / 181	−3.3
6	56,547	2486.2	− 2552	−65.8	× 27 / 181	−9.8
7	56,548	2512.4	− 2567	−54.6	× 25 / 181	−7.5
8	56,550	2502.9	− 2586	−83.1	× 35 / 181	−16.1
Sum, rounded to a whole point						−37

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	52,522	2464.1	− 2436	28.1	× 25 / 173	4.1
4	52,523	2489.3	− 2485	4.3	× 32 / 173	0.8
5	52,525	2513.7	− 2528	−14.3	× 26 / 173	−2.1
6	52,527	2508.6	− 2552	−43.4	× 39 / 173	−9.8
7	52,529	2482.8	− 2567	−84.2	× 23 / 173	−11.2
8	52,531	2548.5	− 2586	−37.5	× 28 / 173	−6.1
Sum, rounded to a whole point						−24

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,030	2486.8	− 2436	50.8	× 24 / 177	6.9
4	54,032	2480.3	− 2485	−4.7	× 29 / 177	−0.8
5	54,035	2507.6	− 2528	−20.4	× 34 / 177	−3.9
6	54,036	2526.5	− 2552	−25.5	× 28 / 177	−4
7	54,038	2506.5	− 2567	−60.5	× 39 / 177	−13.3
8	54,040	2490.3	− 2586	−95.7	× 23 / 177	−12.4
Sum, rounded to a whole point						−28

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,140	2498.7	− 2436	62.7	× 19 / 153	7.8
4	54,141	2496.4	− 2485	11.4	× 21 / 153	1.6
5	54,144	2513.8	− 2528	−14.2	× 28 / 153	−2.6
6	54,145	2497.3	− 2552	−54.7	× 24 / 153	−8.6
7	54,148	2531.7	− 2567	−35.3	× 24 / 153	−5.5
8	54,149	2523.0	− 2586	−63	× 37 / 153	−15.2
Sum, rounded to a whole point						−23

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,381	2479.3	− 2436	43.3	× 20 / 133	6.5
4	54,382	2496.0	− 2485	11	× 21 / 133	1.7
5	54,383	2536.9	− 2528	8.9	× 15 / 133	1
6	54,384	2503.6	− 2552	−48.4	× 29 / 133	−10.6
7	54,385	2526.9	− 2567	−40.1	× 20 / 133	−6
8	54,386	2516.0	− 2586	−70	× 28 / 133	−14.7
Sum, rounded to a whole point						−22

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,427	2429.9	− 2436	−6.1	× 19 / 109	−1.1
4	54,428	2447.7	− 2485	−37.3	× 22 / 109	−7.5
5	54,429	2448.9	− 2528	−79.1	× 22 / 109	−16
6	54,430	2468.1	− 2552	−83.9	× 15 / 109	−11.5
7	54,431	2470.2	− 2567	−96.8	× 13 / 109	−11.5
8	54,432	2505.8	− 2586	−80.2	× 18 / 109	−13.2
Sum, rounded to a whole point						−61

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,376	2418.8	− 2436	−17.2	× 32 / 133	−4.1
4	54,377	2486.5	− 2485	1.5	× 22 / 133	0.2
5	54,378	2477.1	− 2528	−50.9	× 22 / 133	−8.4
6	54,379	2465.7	− 2552	−86.3	× 29 / 133	−18.8
7	54,380	2457.5	− 2567	−109.5	× 14 / 133	−11.5
8	54,381	2515.4	− 2586	−70.6	× 14 / 133	−7.4
Sum, rounded to a whole point						−50

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,248	2400.4	− 2436	−35.6	× 20 / 126	−5.7
4	54,249	2452.3	− 2485	−32.7	× 29 / 126	−7.5
5	54,250	2427.1	− 2528	−100.9	× 19 / 126	−15.2
6	54,251	2437.9	− 2552	−114.1	× 23 / 126	−20.8
7	54,252	2466.9	− 2567	−100.1	× 20 / 126	−15.9
8	54,253	2452.9	− 2586	−133.1	× 15 / 126	−15.8
Sum, rounded to a whole point						−81

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	53,986	2424.5	− 2436	−11.5	× 11 / 120	−1.1
4	53,987	2424.1	− 2485	−60.9	× 19 / 120	−9.6
5	53,988	2432.2	− 2528	−95.8	× 32 / 120	−25.5
6	53,989	2462.5	− 2552	−89.5	× 18 / 120	−13.4
7	53,990	2474.5	− 2567	−92.5	× 19 / 120	−14.6
8	53,991	2471.6	− 2586	−114.4	× 21 / 120	−20
Sum, rounded to a whole point						−84

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −37, −24, −28, −23, −22, −61, −50, −81, −84 → −45.6
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 13 · 2016→2017: 4 · 2017→2018: 5 · 2018→2019: 1 · 2019→2022: 39 · 2022→2023: 11 · 2023→2024: 31 · 2024→2025: 3 → average 13.4
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 13.4 × 2.66 = 35.6. Upper limit −10, lower limit −81.2.

Why 2.66? It is the standard factor from quality control, the work of Walter Shewhart and W. Edwards Deming. It turns "how much the result typically changes in a year" into "how far it can wander by chance alone".

Years with no result (no state tests were given in spring 2020) are skipped: the year-to-year change runs from the last year with a result to the next one.

Step 3 · Free or reduced-price meals

The share of enrolled students eligible for free or reduced-price meals. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.